Scalar perturbation theory is a well-established theory to study perturbations in a given system [1]}. This theory, as developed and presented here, provides a convenient and useful framework to explore the impact of ellipticity. A generic but vital feature in the use of this theory is the negligibility of the polarization effects, especially the spin-orbit interaction that gives rise to differences in the propagation constants of the vector modes, \(HE_{l+1,m}\)  and \(EH_{l-1,m}\) . In this work, we subsequently explore the effect of spin-orbit interaction to estimate bounds on the values of ellipticity for which the derived results are most valid (accurate). The validity range expands with increasing values of normalized frequency, \(V\) , as in a multimode fiber (larger core radius implies relatively smaller spin-orbit interaction), and dwindles as the topological charge is increased, consistent with the fact that the spin-orbit interaction becomes significant at higher values of \(l\)  and thus cannot be ignored. As a result, the numerical results based on the developed theory are most accurate for low values of topological charge (as determined by the fiber parameters). We have illustrated the utility of the analytic expressions and their validity with application to a step-index few mode fiber and a multimode fiber.
